Question

Find the roots of the following equations, if they exist, by applying the quadratic formula:

x² - 2ax - (4b² - a²) = 0

Answer 1

The given equations is x² - 2ax - (4b² - a²) = 0

Comparing it with Ax² + Bx + C = 0.we get

A = 1, B = -2a and C = - (4b² - a²)

∴ Discriminant D = B² - 4AC = (-2a)² - 4 x 1 x [-(4b² - a²)] = 4a² +  16b² - 4a² = 16b² >0

So, the given equation has real roots

Now, √D = \(\sqrt{16b^2}\) = 4b

Hence, a + 2b and a - 2b are the roots of the given equation.